a) Any idea if I can make just a couple of gallons in a 5 gallon glass carboy? i.e., would the extra airspace be too much?
For fermenting, this should be fine, as the yeast activity will produce enough CO2 to keep the air off of your hooch. For bulk aging, you would want an appropriately sized container to reduce the headspace and exposure to oxygen.
b) Once bottled, how do you store it? I.e., can the bottles stand upright, or do they have to be lying on their sides? Is corking them good?
If you cork it in wine bottles, treat it like wine. You'll need to degas it before corking. I have also had good results bottling it (with priming sugar for carbonation) in 16 oz "woozy" bottles with poly caps, or in regular beer bottles, both of which you would store upright.
c) How much does temperature affect the outcome? Is making it this time of year a good idea?
The type of yeast you use drives the fermentation temperature. I keep my fermentation area at 65 - 72 F year round, and that works for most wine yeast. Once bottled, store it somewhere cool and dark. A quick Google search will yield more articles on this than one has time to read.
d) What is the general timetable for a batch of this?
After primary fermentation (4 - 6 weeks), rack it to another container for bulk aging, or bottle it, but wait at least 2 weeks before consumption, the longer the better. I have remnants of almost every batch I have made, with the oldest being around 7 months. I will be trying that one soon.
Good luck to your forum friend!